In [2]:
import sys
sys.setrecursionlimit(10000)
import warnings
warnings.filterwarnings('ignore', category=DeprecationWarning)
In [3]:
import cPickle
import gzip

from breze.learn.data import one_hot
from breze.learn.base import cast_array_to_local_type
from breze.learn.utils import tile_raster_images

import climin.stops
import climin.initialize

from breze.learn import hvi
from breze.learn.hvi import HmcViModel
from breze.learn.hvi.energies import (NormalGaussKinEnergyMixin, DiagGaussKinEnergyMixin)
from breze.learn.hvi.inversemodels import MlpGaussInvModelMixin

from matplotlib import pyplot as plt
from matplotlib import cm

import numpy as np

#import fasttsne

from IPython.html import widgets
%matplotlib inline

import theano
theano.config.compute_test_value = 'ignore'#'raise'
from theano import (tensor as T, clone)

Couldn't import dot_parser, loading of dot files will not be possible.

//anaconda/lib/python2.7/site-packages/IPython/html.py:14: ShimWarning: The `IPython.html` package has been deprecated. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.
  "`IPython.html.widgets` has moved to `ipywidgets`.", ShimWarning)
In [4]:
datafile = '../mnist.pkl.gz'
# Load data.                                                                                                   

with gzip.open(datafile,'rb') as f:                                                                        
    train_set, val_set, test_set = cPickle.load(f)                                                       

X, Z = train_set                                                                                               
VX, VZ = val_set
TX, TZ = test_set

Z = one_hot(Z, 10)
VZ = one_hot(VZ, 10)
TZ = one_hot(TZ, 10)

X_no_bin = X
VX_no_bin = VX
TX_no_bin = TX

# binarize the MNIST data
np.random.seed(0)
X  = np.random.binomial(1, X) * 1.0
VX = np.random.binomial(1, VX) * 1.0
TX = np.random.binomial(1, TX) * 1.0

image_dims = 28, 28

X, Z, VX, VZ, TX, TZ = [cast_array_to_local_type(i) for i in (X, Z, VX,VZ, TX, TZ)]
print X.shape

(50000, 784)
In [5]:
fig, ax = plt.subplots(figsize=(9, 9))

img = tile_raster_images(X[:64], image_dims, (8, 8), (1, 1))
ax.imshow(img, cmap=cm.binary)
Out[5]:
<matplotlib.image.AxesImage at 0x10763b9d0>
In [6]:
fast_dropout = False

if fast_dropout:
    class MyHmcViModel(HmcViModel, 
                   hvi.FastDropoutMlpBernoulliVisibleVAEMixin, 
                   hvi.FastDropoutMlpGaussLatentVAEMixin, 
                   DiagGaussKinEnergyMixin,
                   MlpGaussInvModelMixin):
        pass

    kwargs = {
        'p_dropout_inpt': .1,
        'p_dropout_hiddens': [.2, .2],
    }

    print 'yeah'

else:
    class MyHmcViModel(HmcViModel, 
                   hvi.MlpBernoulliVisibleVAEMixin, 
                   hvi.MlpGaussLatentVAEMixin, 
                   DiagGaussKinEnergyMixin,
                   MlpGaussInvModelMixin):
        pass
    kwargs = {}


batch_size = 200
#optimizer = 'rmsprop', {'step_rate': 1e-4, 'momentum': 0.95, 'decay': .95, 'offset': 1e-6}
#optimizer = 'adam', {'step_rate': .5, 'momentum': 0.9, 'decay': .95, 'offset': 1e-6}
optimizer = 'adam', {'step_rate': 0.001}

# This is the number of random variables NOT the size of 
# the sufficient statistics for the random variables.
n_latents = 2
n_hidden = 200

m = MyHmcViModel(X.shape[1], n_latents, 
                 [n_hidden, n_hidden], ['rectifier'] * 2, 
                 [n_hidden], ['rectifier'] * 1, 
                 [n_hidden], ['rectifier'] * 1,
                 n_hmc_steps=3, n_lf_steps=12,
                 n_z_samples=1,
          optimizer=optimizer, batch_size=batch_size, allow_partial_velocity_update=False, perform_acceptance_step=False,
          **kwargs)

climin.initialize.randomize_normal(m.parameters.data, 0.1, 1e-1)
m.parameters.__setitem__(m.hmc_sampler.step_size_param, 0.01)
#m.parameters.__setitem__(m.kin_energy.mlp.layers[-1].bias, 1)
In [7]:
old_best_params = None
#print m.score(TX)
print m.parameters.data.shape

(514595,)
In [83]:
FILENAME = 'hvi_gen2_recog1_aux1_late2_hid200_fullbin_untrained.pkl'

# In[5]:
#old_best_params = None
f = open(FILENAME, 'rb')
np_array = cPickle.load(f)
old_best_params = cast_array_to_local_type(np_array)
f.close()
print old_best_params.shape

(514595,)
In [84]:
m.parameters.data = old_best_params.copy()
old_best_loss = m.score(VX)
print old_best_loss
print m.score(TX)

140.88735
142.42525
In [70]:
print m.parameters.view(m.init_recog.mlp.layers[1].bias)

[ 0.05071862 -0.16010898 -5.13858843 -7.01162291]
In [ ]:
#m.parameters.__setitem__(m.init_recog.mlp.layers[1].bias, np.array([0.05691881, -0.17896466, -0.08941603, -1.76431561]).astype('float32'))
In [ ]:
#m.parameters.__setitem__(m.hmc_sampler.step_size_param, 0.09)
In [86]:
print 0.1 * m.parameters.view(m.hmc_sampler.step_size_param) ** 2 + 1e-8

[ 0.00081001]
In [87]:
print m.score(TX)
#print m.estimate_nll(TX, 500)

142.505125
In [ ]:
max_passes = 250
max_iter = max_passes * X.shape[0] / batch_size
n_report = X.shape[0] / batch_size

stop = climin.stops.AfterNIterations(max_iter)
pause = climin.stops.ModuloNIterations(n_report)

# theano.config.optimizer = 'fast_compile'

for i, info in enumerate(m.powerfit((X_no_bin,), (VX,), stop, pause, eval_train_loss=False)):
    print i, info['loss'], info['val_loss']
    if i == 0 and old_best_params is not None:
        if info['best_loss'] > old_best_loss:
            info['best_loss'] = old_best_loss
            info['best_pars'] = old_best_params
    
    if info['best_loss'] == info['val_loss']:
        np.savetxt('hvi_short_basic_test.csv', m.parameters.data, delimiter=',')
In [ ]:
print m.score(VX_no_bin)
print m.score(TX_no_bin)
In [88]:
f_z_init_sample = m.function(['inpt'], m.init_recog.sample())
f_z_sample = m.function(['inpt'], m.hmc_sampler.output)
f_gen = m.function([m.gen.inpt], m.gen.sample())
f_gen_rate = m.function([m.gen.inpt], m.gen.rate)
In [89]:
curr_pos = T.matrix('current_position')
curr_vel = T.matrix('current_velocity')
norm_noise = T.matrix('normal_noise')
unif_noise = T.vector('uniform_noise')

new_sampled_vel = m.hmc_sampler.kin_energy.sample(norm_noise)
updated_vel = m.hmc_sampler.partial_vel_constant * curr_vel + m.hmc_sampler.partial_vel_complement * new_sampled_vel
performed_hmc_steps = m.hmc_sampler.perform_hmc_steps(curr_pos, curr_vel)
hmc_step = m.hmc_sampler.hmc_step(curr_pos, curr_vel, np.float32(0), norm_noise, unif_noise)
lf_step_results = m.hmc_sampler.simulate_dynamics(curr_pos, curr_vel, return_full_list=True)

f_pot_en = m.function(['inpt', curr_pos], m.hmc_sampler.eval_pot_energy(curr_pos))
f_kin_en = m.function(['inpt', curr_vel], m.kin_energy.nll(curr_vel).sum(-1))
f_perform_hmc_steps = m.function(['inpt', curr_pos, curr_vel], 
                                T.concatenate([performed_hmc_steps[0], performed_hmc_steps[1]], axis=1))
f_hmc_step = m.function(['inpt', curr_pos, curr_vel, norm_noise, unif_noise], 
                        T.concatenate([hmc_step[0], hmc_step[1]],axis=1), on_unused_input='warn')
f_kin_energy_sample_from_noise = m.function(['inpt', norm_noise], new_sampled_vel)
f_updated_vel_from_noise = m.function(['inpt', curr_vel, norm_noise], updated_vel)
f_perform_lf_steps = m.function(['inpt', curr_pos, curr_vel],
                               T.concatenate([lf_step_results[0], lf_step_results[1]], axis=0))
In [90]:
f_z_init_mean = m.function(['inpt'], m.init_recog.mean)
f_z_init_var = m.function(['inpt'], m.init_recog.var)

f_v_init_var = m.function(['inpt'], m.kin_energy.var)

full_sample = m.hmc_sampler.sample_with_path()
f_full_sample = m.function(['inpt'], T.concatenate([full_sample[0], full_sample[1]], axis=1))
In [91]:
final_pos = T.matrix('final_pos')
final_vel = T.matrix('final_vel')
inpt_replacements = {m.final_vel_model_inpt['position']: final_pos,
                     m.final_vel_model_inpt['time']: T.cast(m.hmc_sampler.n_hmc_steps, dtype='float32')}

final_vel_model_var = clone(m.final_vel_model.var, replace=inpt_replacements)
final_vel_model_mean = clone(m.final_vel_model.mean, replace=inpt_replacements)
final_vel_model_nll = clone(m.final_vel_model.nll(final_vel).sum(-1), replace=inpt_replacements)

f_v_final_var = m.function(['inpt', final_pos], final_vel_model_var)
f_v_final_mean = m.function(['inpt', final_pos], final_vel_model_mean)
f_v_final_model_nll = m.function(['inpt', final_pos, final_vel], final_vel_model_nll)
In [92]:
f_init_recog_nll = m.function(['inpt'], m.init_recog.expected_nll.sum(-1))
In [93]:
print f_init_recog_nll(X).mean()

-7.72047
In [94]:
fig, axs = plt.subplots(3, 3, figsize=(27, 27))

### Original data

O = (X_no_bin[:64])[:, :784].astype('float32')
img = tile_raster_images(O, image_dims, (8, 8), (1, 1))
axs[0, 0].imshow(img, cmap=cm.binary)

O2 = (X[:64])[:, :784].astype('float32')
img = tile_raster_images(O2, image_dims, (8, 8), (1, 1))
axs[1, 0].imshow(img, cmap=cm.binary)

### Reconstruction

#z_sample = f_z_sample((X[:64]))
z_init_sample = f_z_init_sample((X[:64]))
z_sample = f_perform_hmc_steps((X[:64]), 
                               z_init_sample, 
                               f_kin_energy_sample_from_noise((X[:64]), 
                                                              np.random.normal(size=(64, m.n_latent)).astype('float32'))
                               )[-1, :64, :]

R = f_gen_rate(z_sample)[:, :784].astype('float32')
img = tile_raster_images(R, image_dims, (8, 8), (1, 1))
axs[0, 1].imshow(img, cmap=cm.binary)

Rinit = f_gen_rate(z_init_sample)[:, :784].astype('float32')
img = tile_raster_images(Rinit, image_dims, (8, 8), (1, 1))
axs[0, 2].imshow(img, cmap=cm.binary)

R2 = f_gen(z_sample)[:, :784].astype('float32')
img = tile_raster_images(R2, image_dims, (8, 8), (1, 1))
axs[1, 1].imshow(img, cmap=cm.binary)

Rinit2 = f_gen(z_init_sample)[:, :784].astype('float32')
img = tile_raster_images(Rinit2, image_dims, (8, 8), (1, 1))
axs[1, 2].imshow(img, cmap=cm.binary)


### Sampling

prior_sample = np.random.randn(64, m.n_latent).astype('float32')

S = f_gen_rate(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S, image_dims, (8, 8), (1, 1))
axs[2, 0].imshow(img, cmap=cm.binary)

S2 = f_gen(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S2, image_dims, (8, 8), (1, 1))
axs[2, 1].imshow(img, cmap=cm.binary)

#S3 = f_gen_rate(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S, image_dims, (8, 8), (1, 1))
axs[2, 2].imshow(img, cmap=cm.nipy_spectral)
Out[94]:
<matplotlib.image.AxesImage at 0x1188ba650>
In [20]:
from scipy.stats import norm as normal_distribution

unit_interval_positions = np.linspace(0.025, 0.975, 20)
positions = normal_distribution.ppf(unit_interval_positions)
print unit_interval_positions
print positions

latent_array = np.zeros((400, 2))

latent_array[:, 1] = -np.repeat(positions, 20)  # because images are filled top -> bottom, left -> right (row by row)
latent_array[:, 0] = np.tile(positions, 20)
        
fig, axs = plt.subplots(1, 1, figsize=(24, 24))

F = f_gen_rate(latent_array.astype('float32'))

img = tile_raster_images(F, image_dims, (20, 20), (1, 1))
#axs.imshow(img, cmap=cm.nipy_spectral)
axs.imshow(img, cmap=cm.binary)

[ 0.025  0.075  0.125  0.175  0.225  0.275  0.325  0.375  0.425  0.475
  0.525  0.575  0.625  0.675  0.725  0.775  0.825  0.875  0.925  0.975]
[-1.95996398 -1.43953147 -1.15034938 -0.93458929 -0.75541503 -0.59776013
 -0.45376219 -0.31863936 -0.18911843 -0.06270678  0.06270678  0.18911843
  0.31863936  0.45376219  0.59776013  0.75541503  0.93458929  1.15034938
  1.43953147  1.95996398]
Out[20]:
<matplotlib.image.AxesImage at 0x12871fd10>
In [21]:
L = f_z_sample(X)
L_init = f_z_init_sample(X)
In [95]:
X_index = 39  # index=0 -> 5, index=1 -> 0, index=2 -> 4, index=3 -> 1
num_repeats = 1000
In [96]:
print f_z_init_mean(np.array([X[X_index, :]]))
print f_z_init_var(np.array([X[X_index, :]]))
print f_v_init_var(np.array([X[X_index, :]]))
#print f_v_final_var(np.array(X[:2]))
#print f_v_final_mean(np.array(X[:2]))

[[ 0.05511833 -0.09898119]]
[[  4.99626003e-05   1.97342451e-04]]
[[ 0.99275988  0.99601656]]
In [97]:
repeated_X = np.tile(np.array([X[X_index, :]]), (num_repeats, 1)).astype('float32')

full_sample = f_full_sample(repeated_X)
z_samples = full_sample[:, :num_repeats, :]
v_samples = full_sample[:, num_repeats:, :]

z_sample_final_mean = z_samples[m.n_hmc_steps, :, :].mean(axis=0)
z_sample_final_std = z_samples[m.n_hmc_steps, :, :].std(axis=0)
In [98]:
print z_sample_final_mean
print z_sample_final_std ** 2

[ 0.07491784 -0.05287353]
[ 0.00074608  0.0003744 ]
In [99]:
dim1 = 0
dim2 = 1
In [29]:
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(L[:, dim1], L[:, dim2], c=Z[:].argmax(1), lw=0, s=5, alpha=.2)
axs[1].scatter(L_init[:, dim1], L_init[:, dim2], c=Z[:].argmax(1), lw=0, s=5, alpha=.2)

cax = fig.add_axes([0.95, 0.2, 0.02, 0.6])
cax.scatter(np.repeat(0, 10), np.arange(10), c=np.arange(10), lw=0, s=300)
cax.set_xlim(-0.1, 0.1)
cax.set_ylim(-0.5, 9.5)
plt.yticks(np.arange(10))
plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')
cax.tick_params(axis='y', colors='white')
for tick in cax.yaxis.get_major_ticks():
    tick.label.set_fontsize(14)
    tick.label.set_color('black')
    
cax.spines['bottom'].set_color('white')
cax.spines['top'].set_color('white') 
cax.spines['right'].set_color('white')
cax.spines['left'].set_color('white')

axs[0].set_title('After HMC steps')
axs[1].set_title('Initial recognition model')

axs[0].set_xlim(-3, 3)
axs[0].set_ylim(-3, 3)
axs[1].set_xlim(-3, 3)
axs[1].set_ylim(-3, 3)
Out[29]:
(-3, 3)
In [30]:
fig, axs = plt.subplots(4, 5, figsize=(20, 16))
colors = cm.jet(np.linspace(0, 1, 10))
for i in range(5):
    axs[0, i].scatter(L_init[Z[:].argmax(1) == i, dim1], L_init[Z[:].argmax(1) == i, dim2], c=colors[i], lw=0, s=5, alpha=.2)
    axs[1, i].scatter(L[Z[:].argmax(1) == i, dim1], L[Z[:].argmax(1) == i, dim2], c=colors[i], lw=0, s=5, alpha=.2)
    axs[0, i].set_title(str(i) + ' before HMC')
    axs[1, i].set_title(str(i) + ' after HMC')
    axs[2, i].scatter(L_init[Z[:].argmax(1) == (5+i), dim1], L_init[Z[:].argmax(1) == (5+i), dim2], c=colors[5+i], lw=0, s=5, alpha=.2)
    axs[3, i].scatter(L[Z[:].argmax(1) == (5+i), dim1], L[Z[:].argmax(1) == (5+i), dim2], c=colors[5+i], lw=0, s=5, alpha=.2)
    axs[2, i].set_title(str(5+i) + ' before HMC')
    axs[3, i].set_title(str(5+i) + ' after HMC')
    for j in range(4):
        axs[j, i].set_xlim(-3, 3)
        axs[j, i].set_ylim(-3, 3)
In [120]:
resolution = 200
lower_dim1_limit = z_sample_final_mean[dim1] - 0.2
upper_dim1_limit = z_sample_final_mean[dim1] + 0.2
lower_dim2_limit = z_sample_final_mean[dim2] - 0.4
upper_dim2_limit = z_sample_final_mean[dim2] + 0.4

pot_energy_matrix = np.zeros((resolution, resolution), dtype='float32')
x = cast_array_to_local_type(np.linspace(lower_dim1_limit, upper_dim1_limit, resolution))
y = cast_array_to_local_type(np.linspace(lower_dim2_limit, upper_dim2_limit, resolution))
for i in range(resolution):
    for j in range(resolution):
        #pos_array = f_z_init_mean(np.array([X[X_index, :]]))
        pos_array = np.array([z_sample_final_mean])
        pos_array[0, dim1] = x[i]
        pos_array[0, dim2] = y[j]
        pot_energy_matrix[j, i] = f_pot_en(np.array([X[X_index, :]]), pos_array)

print pot_energy_matrix.min()
print pot_energy_matrix.max()        

fig, ax = plt.subplots(1, 1, figsize=(9, 9))
CS = ax.contour(x, y, pot_energy_matrix, 20)
plt.clabel(CS, inline=1, fmt='%1.0f', fontsize=10)
plt.show()

160.224
331.957
In [114]:
resolution = 200
underlying_variance = f_v_init_var(np.array([X[X_index, :]]))
velocity_range_for_images = 10.0 * np.sqrt(underlying_variance[0, :])
lower_dim1_limit = np.around(- velocity_range_for_images[dim1])
upper_dim1_limit = np.around(  velocity_range_for_images[dim1])
lower_dim2_limit = np.around(- velocity_range_for_images[dim2])
upper_dim2_limit = np.around(  velocity_range_for_images[dim2])

kin_energy_matrix = np.zeros((resolution, resolution), dtype='float32')
kin_x = cast_array_to_local_type(np.linspace(lower_dim1_limit, upper_dim1_limit, resolution))
kin_y = cast_array_to_local_type(np.linspace(lower_dim2_limit, upper_dim2_limit, resolution))
for i in range(resolution):
    for j in range(resolution):
        vel_array = np.zeros((1, m.n_latent)).astype('float32')
        vel_array[0, dim1] = kin_x[i]
        vel_array[0, dim2] = kin_y[j]
        kin_energy_matrix[j, i] = f_kin_en(np.array([X[X_index, :]]), vel_array)

print kin_energy_matrix.min()
print kin_energy_matrix.max()
        
fig, ax = plt.subplots(1, 1, figsize=(9, 9))
CS = ax.contour(kin_x, kin_y, kin_energy_matrix)
plt.clabel(CS, inline=1, fmt='%1.1f', fontsize=10)
plt.show()

1.83479
102.397
In [125]:
fig, axs = plt.subplots(m.n_hmc_steps + 1, 3, figsize=(18, (m.n_hmc_steps + 1) * 6))
colors = cm.jet(np.linspace(0, 1, 10))

#contour_levels = (198, 200, 202, 204, 206, 208, 210)
#contour_levels = (130, 140, 150, 160, 180, 200, 240, 280)
#contour_levels = (180, 190, 200, 220, 240, 260, 280, 300, 320)
#contour_levels = (400, 402, 404, 406, 408, 410, 412, 416, 420)
#contour_levels = (106, 108, 110, 112, 114, 116, 118, 120, 124, 128)
contour_levels = (160, 165, 170, 175, 180, 185, 190, 195, 200, 210, 220, 230, 240, 250, 270, 300)
#contour_levels = (174, 175, 176, 177, 178, 180, 182, 184, 186, 190, 200)
#contour_levels = (59, 61, 63, 65, 67, 69, 71, 73, 75, 80, 85, 90)

vel_contour_levels = np.linspace(2.0, 70.0, 18)
#CS0 = axs[0, 0].contourf(x, y, pot_energy_matrix, np.linspace(155, 240, 500))

def colour_for_z_samples(samples):
    mean = samples.mean(axis=0)
    mean1 = mean[dim1]
    mean2 = mean[dim2]
    colour = np.zeros_like(samples[:, 0])
    colour[np.logical_and(samples[:, dim1] < mean1,  samples[:, dim2] < mean2)] = 0
    colour[np.logical_and(samples[:, dim1] < mean1,  samples[:, dim2] >= mean2)] = 2
    colour[np.logical_and(samples[:, dim1] >= mean1, samples[:, dim2] < mean2)] = 4
    colour[np.logical_and(samples[:, dim1] >= mean1, samples[:, dim2] >= mean2)] = 7
    colour[((samples[:, dim1] - mean1) ** 2 + (samples[:, dim2] - mean2) ** 2) < 1e-5] = 9
    return colour.astype('int32')

colour = colour_for_z_samples(z_samples[m.n_hmc_steps,:,:])
print v_samples[m.n_hmc_steps, colour == 0, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 2, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 4, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 7, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 9, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 0, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 2, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 4, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 7, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 9, :].var(axis=0)


for i in range(m.n_hmc_steps + 1):
    CS = axs[i, 0].contour(x, y, pot_energy_matrix, contour_levels)
    plt.clabel(CS, inline=1, fmt='%1.0f', fontsize=10)
    axs[i, 0].scatter(z_samples[i,:,dim1], z_samples[i,:,dim2], c=colors[colour_for_z_samples(z_samples[i,:,:])], s=20, alpha=.3, lw=0)
    
    CS_vel = axs[i, 1].contour(kin_x, kin_y, kin_energy_matrix, vel_contour_levels)
    plt.clabel(CS_vel, inline=1, fmt='%1.1f', fontsize=10)
    axs[i, 1].scatter(v_samples[i,:,dim1], v_samples[i,:,dim2], c=colors[colour_for_z_samples(z_samples[i,:,:])], s=20, alpha=.3, lw=0)
    
    pot_energy_distrib = f_pot_en(repeated_X, z_samples[i, :, :])
    pot_energy_distrib_mean = pot_energy_distrib.mean()
    axs[i, 2].hist(pot_energy_distrib, 50, normed=1, range=(np.floor(pot_energy_matrix.min()), contour_levels[-1]))
    axs[i, 2].axvline(pot_energy_distrib_mean, color='r', linestyle='dashed', linewidth=2)
    axs[i, 2].text(pot_energy_distrib_mean + 1.0, 0.8*axs[i, 2].get_ylim()[1], 'Mean: ' + str(pot_energy_distrib_mean))
    axs[i, 1].set_xlim(-velocity_range_for_images[dim1], velocity_range_for_images[dim1])
    axs[i, 1].set_ylim(-velocity_range_for_images[dim2], velocity_range_for_images[dim2])


print pot_energy_matrix.min()
print pot_energy_matrix.max()
axs[0, 0].scatter(f_z_init_mean(np.array([X[X_index,:]]))[0, dim1], f_z_init_mean(np.array([X[X_index,:]]))[0, dim2], c='black', s=20)

plt.show()

[ 0.1089168  0.3906014]
[-0.00914347  0.29671502]
[ 1.29553545 -0.1168554 ]
[ 1.61746216  0.04021918]
[ 4.18673182  0.62475199]
[ 3.05368781  1.00487351]
[ 3.733495    1.23304033]
[ 2.15984344  1.46097982]
[ 2.51078868  1.56722975]
[ 0.  0.]
160.224
331.957
In [66]:
np.random.seed(1)

velocity_noise = np.random.normal(size=(m.n_hmc_steps, 1, m.n_latent)).astype('float32')

single_X = np.array([X[X_index, :]])
init_pos = f_z_init_mean(single_X)
init_vel = f_kin_energy_sample_from_noise(single_X, velocity_noise[0])

num_vels_per_hmc = (m.n_lf_steps + 2)

position_array = np.zeros((m.n_hmc_steps * m.n_lf_steps + 1, m.n_latent))
position_array[0] = init_pos
velocity_array = np.zeros((m.n_hmc_steps * num_vels_per_hmc, m.n_latent))
velocity_array[0] = init_vel

for hmc_num in range(m.n_hmc_steps):
    if hmc_num == 0:
        curr_pos = init_pos
        curr_vel = init_vel
    else:
        curr_vel = f_updated_vel_from_noise(single_X, curr_vel, velocity_noise[hmc_num])
        velocity_array[hmc_num * (m.n_lf_steps + 2)] = curr_vel
    
    lf_step_results = f_perform_lf_steps(single_X, curr_pos, curr_vel)
    pos_steps = lf_step_results[:m.n_lf_steps]
    vel_half_steps_and_final = lf_step_results[m.n_lf_steps:]
    final_vel = lf_step_results[-1]
    final_pos = pos_steps[-1]
    
    position_array[hmc_num * m.n_lf_steps + 1: (hmc_num + 1)*m.n_lf_steps + 1] = pos_steps[:, 0, :]
    velocity_array[hmc_num * num_vels_per_hmc + 1: (hmc_num + 1) * num_vels_per_hmc] = vel_half_steps_and_final[:, 0, :]
    
    curr_pos = final_pos
    curr_vel = final_vel
In [126]:
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
step_color = cm.jet(np.linspace(0, 1, position_array.shape[0]))
CS = axs[0].contour(x, y, pot_energy_matrix, contour_levels)
CS_vel = axs[1].contour(kin_x, kin_y, kin_energy_matrix, vel_contour_levels)
hmc_step_indices = np.arange(0, position_array.shape[0], m.n_lf_steps)
size_array = 40*np.ones((position_array.shape[0],))
size_array[hmc_step_indices] = 100
axs[0].scatter(position_array[:, dim1], position_array[:, dim2], c=step_color, lw=1, s=size_array)
axs[1].set_color_cycle(step_color)

for hmc_num in range(m.n_hmc_steps):
    curr_vel_range = np.arange(num_vels_per_hmc * hmc_num, num_vels_per_hmc * (hmc_num + 1) - 2)
    init_vel_ind = hmc_num * num_vels_per_hmc
    final_vel_ind = (hmc_num + 1) * num_vels_per_hmc - 1
    curr_index = hmc_step_indices[hmc_num]
    next_index = hmc_step_indices[hmc_num + 1]
    for j in curr_vel_range:
        axs[1].plot(velocity_array[j:j+2, dim1], velocity_array[j:j+2, dim2], lw=2)
    axs[1].scatter(velocity_array[init_vel_ind, dim1], velocity_array[init_vel_ind, dim2], c=step_color[curr_index], lw=0, s=100)
    axs[1].scatter(velocity_array[final_vel_ind, dim1], velocity_array[final_vel_ind, dim2], c=step_color[next_index], lw=0, s=100)

for hmc_num in range(m.n_hmc_steps):
    final_vel_ind = (hmc_num + 1) * num_vels_per_hmc - 1
    next_index = hmc_step_indices[hmc_num + 1]
    axs[1].plot(velocity_array[final_vel_ind-1:final_vel_ind+1, dim1], velocity_array[final_vel_ind-1:final_vel_ind+1, dim2], lw=2, c=step_color[next_index])

Auxiliary model for the final velocity

In [ ]:
variation_start = z_sample_final_mean - 2*z_sample_final_std
variation_end = z_sample_final_mean + 2*z_sample_final_std

final_vel_model_mean_output = np.zeros((m.n_latent, num_repeats, m.n_latent))
final_vel_model_var_output = np.zeros((m.n_latent, num_repeats, m.n_latent))

for variation_dim in range(m.n_latent):
    z_variation = np.linspace(variation_start[variation_dim], variation_end[variation_dim], num_repeats)
    sample_array = np.tile(z_sample_final_mean, (num_repeats, 1))
    sample_array[:, variation_dim] = z_variation
    final_vel_model_mean_output[variation_dim] = f_v_final_mean(repeated_X, sample_array)
    final_vel_model_var_output[variation_dim] = f_v_final_var(repeated_X, sample_array)
In [ ]:
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(final_vel_model_mean_output[:, :, dim1], 
           final_vel_model_mean_output[:, :, dim2],  
           c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
           lw=0, s=5)
axs[1].scatter(final_vel_model_var_output[:, :, dim1], 
           final_vel_model_var_output[:, :, dim2],  
           c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
           lw=0, s=5)

plt.show()
In [ ]:
final_vel_mean = f_v_final_mean(repeated_X, z_samples[3, :, :])
final_vel_var = f_v_final_var(repeated_X, z_samples[3, :, :])
final_vel_nll = f_v_final_model_nll(repeated_X, z_samples[3, :, :], v_samples[3, :, :])
In [ ]:
fig, axs = plt.subplots(4, 2, figsize=(18, 36))
# TODO: Analysis of how final_vel_mean and final_vel_var depend on z (since they all share the same x)

print z_samples[3, :, :].mean(axis=0)
print z_samples[3, :, :].var(axis=0)
print v_samples[3, :, :].mean(axis=0)
print v_samples[3, :, :].var(axis=0)
print f_v_init_var(np.array([X[X_index, :]]))

print final_vel_nll.mean()
plt.boxplot(final_vel_nll, whis=1)
plt.show()
In [ ]:
centers = np.zeros((10,n_latents))
stddevs = np.zeros((10,n_latents))
centers_init = np.zeros((10,n_latents))
stddevs_init = np.zeros((10,n_latents))
for i in range(10):
    Li = f_z_sample(X[Z.argmax(1) == i])
    centers[i] = Li.mean(axis=0)
    stddevs[i] = np.std(Li, axis=0)
    
    Li_init = f_z_init_sample(X[Z.argmax(1) == i])
    centers_init[i] = Li_init.mean(axis=0)
    stddevs_init[i] = np.std(Li_init, axis=0)
In [ ]:
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(centers[:, dim1], centers[:, dim2], c=range(10), s=50)
axs[0].scatter(centers_init[:, dim1], centers_init[:, dim2], c=range(10), s=50, marker=u's')

axs[1].scatter(centers[:, dim1], centers[:, dim2], c=range(10), s=50)
axs[1].scatter(centers[:, dim1] + stddevs[:, dim1], centers[:, dim2], c=range(10), s=50, marker=u'>')
axs[1].scatter(centers[:, dim1] - stddevs[:, dim1], centers[:, dim2], c=range(10), s=50, marker=u'<')
axs[1].scatter(centers[:, dim1], centers[:, dim2] + stddevs[:, dim2], c=range(10), s=50, marker=u'^')
axs[1].scatter(centers[:, dim1], centers[:, dim2] - stddevs[:, dim2], c=range(10), s=50, marker=u'v')

#axs[0].set_xlim(-1.2, 1.2)
#axs[0].set_ylim(-1.2, 1.2)
#axs[1].set_xlim(-1.2, 1.2)
#axs[1].set_ylim(-1.2, 1.2)

print (centers[:, dim1] - centers_init[:, dim1])
print (centers[:, dim2] - centers_init[:, dim2])
print (stddevs[:, dim1] - stddevs_init[:, dim1])
print (stddevs[:, dim2] - stddevs_init[:, dim2])
In [ ]: